Complex Surfaces With Many Algebraic Structures

Explore complex surfaces with multiple algebraic structures in this lecture by Anna Abasheva from the Hausdorff Center for Mathematics. Delve into the GAGA principle and its limitations for non-compact varieties, examining Serre's counter-example. Discover a new example of a complex surface with countably many algebraic structures, involving the blowup of a projective plane and the removal of an elliptic curve's strict preimage. Learn about the Hopf transform and its role in constructing alternative algebraic structures by replacing neighborhoods of elliptic curves. Gain insights into the intricate relationship between complex geometry and algebraic varieties in this hour-long presentation.